Date: Monday, December 04, 2017
Location: 3866 East Hall (4:00 PM to 5:00 PM)
Title: Reduced words and EdelmanGreene insertion
Abstract: Every permutation can be written as a product of the simple transpositions s_i, where s_i interchanges i and i+1. Given a permutation w, an expression w = s_{i_1} \cdots s_{i_k} is called a reduced word for w if k is the minimum number of simple transpositions needed to express w. This definition leads an enumerative combinatorialist to ask: How many reduced words are there for a given permutation?
To address this question, Stanley introduced a new type of symmetric function. Edelman and Greene developed an insertion algorithm (similar to RSK) to decompose Stanley's symmetric functions into Schur functions, leading to a solution of the original problem. I will define Schur functions and Stanley's symmetric functions, explain the insertion algorithm, and give a formula for the number of reduced words of the longest permutation in S_n.
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Speaker: Gabriel Frieden
Institution: University of Michigan
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